Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this work.In particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the solution.We first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual points.We further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the solution.The procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large gradients.To demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson equation.It has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual points.Moreover,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠalgorithm.This means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the solution.Furthermore,we also employ the similar adaptive sampling technique for the data points of boundary conditions(BCs)if the sharpness of the solution is near the boundary.The result of the L-shape Poisson problem indicates that the present method can significantly improve the efficiency,stability,and accuracy.

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks

The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization.

A data-driven model of drop size prediction based on artificial neural networks using small-scale data sets

An artificial neural network(ANN)method is introduced to predict drop size in two kinds of pulsed columns with small-scale data sets.After training,the deviation between calculate and experimental results are 3.8%and 9.3%,respectively.Through ANN model,the influence of interfacial tension and pulsation intensity on the droplet diameter has been developed.Droplet size gradually increases with the increase of interfacial tension,and decreases with the increase of pulse intensity.It can be seen that the accuracy of ANN model in predicting droplet size outside the training set range is reach the same level as the accuracy of correlation obtained based on experiments within this range.For two kinds of columns,the drop size prediction deviations of ANN model are 9.6%and 18.5%and the deviations in correlations are 11%and 15%.

Multi-Scale-Matching neural networks for thin plate bending problem

Physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation problems.To resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation problems.Inspired by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,respectively.Moreover,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region problems.Numerical results for the thin plate problem validate the proposed method.

Finite-time Prescribed Performance Time-Varying Formation Control for Second-Order Multi-Agent Systems With Non-Strict Feedback Based on a Neural Network Observer

This paper studies the problem of time-varying formation control with finite-time prescribed performance for nonstrict feedback second-order multi-agent systems with unmeasured states and unknown nonlinearities.To eliminate nonlinearities,neural networks are applied to approximate the inherent dynamics of the system.In addition,due to the limitations of the actual working conditions,each follower agent can only obtain the locally measurable partial state information of the leader agent.To address this problem,a neural network state observer based on the leader state information is designed.Then,a finite-time prescribed performance adaptive output feedback control strategy is proposed by restricting the sliding mode surface to a prescribed region,which ensures that the closed-loop system has practical finite-time stability and that formation errors of the multi-agent systems converge to the prescribed performance bound in finite time.Finally,a numerical simulation is provided to demonstrate the practicality and effectiveness of the developed algorithm.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.

Non-crossing Quantile Regression Neural Network as a Calibration Tool for Ensemble Weather Forecasts

Despite the maturity of ensemble numerical weather prediction(NWP),the resulting forecasts are still,more often than not,under-dispersed.As such,forecast calibration tools have become popular.Among those tools,quantile regression(QR)is highly competitive in terms of both flexibility and predictive performance.Nevertheless,a long-standing problem of QR is quantile crossing,which greatly limits the interpretability of QR-calibrated forecasts.On this point,this study proposes a non-crossing quantile regression neural network(NCQRNN),for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing.The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer,which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer,through a triangular weight matrix with positive entries.The empirical part of the work considers a solar irradiance case study,in which four years of ensemble irradiance forecasts at seven locations,issued by the European Centre for Medium-Range Weather Forecasts,are calibrated via NCQRNN,as well as via an eclectic mix of benchmarking models,ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models.Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration,amongst all competitors.Furthermore,the proposed conception to resolve quantile crossing is remarkably simple yet general,and thus has broad applicability as it can be integrated with many shallow-and deep-learning-based neural networks.

Development of a convolutional neural network based geomechanical upscaling technique for heterogeneous geological reservoir

Geomechanical assessment using coupled reservoir-geomechanical simulation is becoming increasingly important for analyzing the potential geomechanical risks in subsurface geological developments.However,a robust and efficient geomechanical upscaling technique for heterogeneous geological reservoirs is lacking to advance the applications of three-dimensional(3D)reservoir-scale geomechanical simulation considering detailed geological heterogeneities.Here,we develop convolutional neural network(CNN)proxies that reproduce the anisotropic nonlinear geomechanical response caused by lithological heterogeneity,and compute upscaled geomechanical properties from CNN proxies.The CNN proxies are trained using a large dataset of randomly generated spatially correlated sand-shale realizations as inputs and simulation results of their macroscopic geomechanical response as outputs.The trained CNN models can provide the upscaled shear strength(R^(2)>0.949),stress-strain behavior(R^(2)>0.925),and volumetric strain changes(R^(2)>0.958)that highly agree with the numerical simulation results while saving over two orders of magnitude of computational time.This is a major advantage in computing the upscaled geomechanical properties directly from geological realizations without the need to perform local numerical simulations to obtain the geomechanical response.The proposed CNN proxybased upscaling technique has the ability to(1)bridge the gap between the fine-scale geocellular models considering geological uncertainties and computationally efficient geomechanical models used to assess the geomechanical risks of large-scale subsurface development,and(2)improve the efficiency of numerical upscaling techniques that rely on local numerical simulations,leading to significantly increased computational time for uncertainty quantification using numerous geological realizations.

Hybrid model for BOF oxygen blowing time prediction based on oxygen balance mechanism and deep neural network

The amount of oxygen blown into the converter is one of the key parameters for the control of the converter blowing process,which directly affects the tap-to-tap time of converter. In this study, a hybrid model based on oxygen balance mechanism (OBM) and deep neural network (DNN) was established for predicting oxygen blowing time in converter. A three-step method was utilized in the hybrid model. First, the oxygen consumption volume was predicted by the OBM model and DNN model, respectively. Second, a more accurate oxygen consumption volume was obtained by integrating the OBM model and DNN model. Finally, the converter oxygen blowing time was calculated according to the oxygen consumption volume and the oxygen supply intensity of each heat. The proposed hybrid model was verified using the actual data collected from an integrated steel plant in China, and compared with multiple linear regression model, OBM model, and neural network model including extreme learning machine, back propagation neural network, and DNN. The test results indicate that the hybrid model with a network structure of 3 hidden layer layers, 32-16-8 neurons per hidden layer, and 0.1 learning rate has the best prediction accuracy and stronger generalization ability compared with other models. The predicted hit ratio of oxygen consumption volume within the error±300 m^(3)is 96.67%;determination coefficient (R^(2)) and root mean square error (RMSE) are0.6984 and 150.03 m^(3), respectively. The oxygen blow time prediction hit ratio within the error±0.6 min is 89.50%;R2and RMSE are0.9486 and 0.3592 min, respectively. As a result, the proposed model can effectively predict the oxygen consumption volume and oxygen blowing time in the converter.

Reliability analysis of slope stability by neural network,principal component analysis,and transfer learning techniques

The prediction of slope stability is considered as one of the critical concerns in geotechnical engineering.Conventional stochastic analysis with spatially variable slopes is time-consuming and highly computation-demanding.To assess the slope stability problems with a more desirable computational effort,many machine learning(ML)algorithms have been proposed.However,most ML-based techniques require that the training data must be in the same feature space and have the same distribution,and the model may need to be rebuilt when the spatial distribution changes.This paper presents a new ML-based algorithm,which combines the principal component analysis(PCA)-based neural network(NN)and transfer learning(TL)techniques(i.e.PCAeNNeTL)to conduct the stability analysis of slopes with different spatial distributions.The Monte Carlo coupled with finite element simulation is first conducted for data acquisition considering the spatial variability of cohesive strength or friction angle of soils from eight slopes with the same geometry.The PCA method is incorporated into the neural network algorithm(i.e.PCA-NN)to increase the computational efficiency by reducing the input variables.It is found that the PCA-NN algorithm performs well in improving the prediction of slope stability for a given slope in terms of the computational accuracy and computational effort when compared with the other two algorithms(i.e.NN and decision trees,DT).Furthermore,the PCAeNNeTL algorithm shows great potential in assessing the stability of slope even with fewer training data.

Customized Convolutional Neural Network for Accurate Detection of Deep Fake Images in Video Collections

The motivation for this study is that the quality of deep fakes is constantly improving,which leads to the need to develop new methods for their detection.The proposed Customized Convolutional Neural Network method involves extracting structured data from video frames using facial landmark detection,which is then used as input to the CNN.The customized Convolutional Neural Network method is the date augmented-based CNN model to generate‘fake data’or‘fake images’.This study was carried out using Python and its libraries.We used 242 films from the dataset gathered by the Deep Fake Detection Challenge,of which 199 were made up and the remaining 53 were real.Ten seconds were allotted for each video.There were 318 videos used in all,199 of which were fake and 119 of which were real.Our proposedmethod achieved a testing accuracy of 91.47%,loss of 0.342,and AUC score of 0.92,outperforming two alternative approaches,CNN and MLP-CNN.Furthermore,our method succeeded in greater accuracy than contemporary models such as XceptionNet,Meso-4,EfficientNet-BO,MesoInception-4,VGG-16,and DST-Net.The novelty of this investigation is the development of a new Convolutional Neural Network(CNN)learning model that can accurately detect deep fake face photos.

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

An End-To-End Hyperbolic Deep Graph Convolutional Neural Network Framework

Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.

A Review of Computing with Spiking Neural Networks

Artificial neural networks(ANNs)have led to landmark changes in many fields,but they still differ significantly fromthemechanisms of real biological neural networks and face problems such as high computing costs,excessive computing power,and so on.Spiking neural networks(SNNs)provide a new approach combined with brain-like science to improve the computational energy efficiency,computational architecture,and biological credibility of current deep learning applications.In the early stage of development,its poor performance hindered the application of SNNs in real-world scenarios.In recent years,SNNs have made great progress in computational performance and practicability compared with the earlier research results,and are continuously producing significant results.Although there are already many pieces of literature on SNNs,there is still a lack of comprehensive review on SNNs from the perspective of improving performance and practicality as well as incorporating the latest research results.Starting from this issue,this paper elaborates on SNNs along the complete usage process of SNNs including network construction,data processing,model training,development,and deployment,aiming to provide more comprehensive and practical guidance to promote the development of SNNs.Therefore,the connotation and development status of SNNcomputing is reviewed systematically and comprehensively from four aspects:composition structure,data set,learning algorithm,software/hardware development platform.Then the development characteristics of SNNs in intelligent computing are summarized,the current challenges of SNNs are discussed and the future development directions are also prospected.Our research shows that in the fields of machine learning and intelligent computing,SNNs have comparable network scale and performance to ANNs and the ability to challenge large datasets and a variety of tasks.The advantages of SNNs over ANNs in terms of energy efficiency and spatial-temporal data processing have been more fully exploited.And the development of programming and deployment tools has lowered the threshold for the use of SNNs.SNNs show a broad development prospect for brain-like computing.

NeurstrucEnergy:A bi-directional GNN model for energy prediction of neural networks in IoT

A significant demand rises for energy-efficient deep neural networks to support power-limited embedding devices with successful deep learning applications in IoT and edge computing fields.An accurate energy prediction approach is critical to provide measurement and lead optimization direction.However,the current energy prediction approaches lack accuracy and generalization ability due to the lack of research on the neural network structure and the excessive reliance on customized training dataset.This paper presents a novel energy prediction model,NeurstrucEnergy.NeurstrucEnergy treats neural networks as directed graphs and applies a bi-directional graph neural network training on a randomly generated dataset to extract structural features for energy prediction.NeurstrucEnergy has advantages over linear approaches because the bi-directional graph neural network collects structural features from each layer's parents and children.Experimental results show that NeurstrucEnergy establishes state-of-the-art results with mean absolute percentage error of 2.60%.We also evaluate NeurstrucEnergy in a randomly generated dataset,achieving the mean absolute percentage error of 4.83%over 10 typical convolutional neural networks in recent years and 7 efficient convolutional neural networks created by neural architecture search.Our code is available at https://github.com/NEUSoftGreenAI/NeurstrucEnergy.git.

Expression Recognition Method Based on Convolutional Neural Network and Capsule Neural Network

Convolutional neural networks struggle to accurately handle changes in angles and twists in the direction of images,which affects their ability to recognize patterns based on internal feature levels. In contrast, CapsNet overcomesthese limitations by vectorizing information through increased directionality and magnitude, ensuring that spatialinformation is not overlooked. Therefore, this study proposes a novel expression recognition technique calledCAPSULE-VGG, which combines the strengths of CapsNet and convolutional neural networks. By refining andintegrating features extracted by a convolutional neural network before introducing theminto CapsNet, ourmodelenhances facial recognition capabilities. Compared to traditional neural network models, our approach offersfaster training pace, improved convergence speed, and higher accuracy rates approaching stability. Experimentalresults demonstrate that our method achieves recognition rates of 74.14% for the FER2013 expression dataset and99.85% for the CK+ expression dataset. By contrasting these findings with those obtained using conventionalexpression recognition techniques and incorporating CapsNet’s advantages, we effectively address issues associatedwith convolutional neural networks while increasing expression identification accuracy.

Assessment of Seasonal Rainfall Prediction in Ethiopia: Evaluating a Dynamic Recurrent Neural Network to Downscale ECMWF-SEAS5 Rainfall

Seasonal rainfall plays a vital role in both environmental dynamics and decision-making for rainfed agriculture in Ethiopia, a country often impacted by extreme climate events such as drought and flooding. Predicting the onset of the rainy season and providing localized rainfall forecasts for Ethiopia is challenging due to the changing spatiotemporal patterns and the country's rugged topography. The Climate Hazards Group Infra Red Precipitation with Station Data(CHIRPS), ERA5-Land total precipitation and temperature data are used from 1981–2022 to predict spatial rainfall by applying an artificial neural network(ANN). The recurrent neural network(RNN) is a nonlinear autoregressive network with exogenous input(NARX), which includes feed-forward connections and multiple network layers, employing the Levenberg Marquart algorithm. This method is applied to downscale data from the European Centre for Medium-range Weather Forecasts fifth-generation seasonal forecast system(ECMWF-SEAS5) and the Euro-Mediterranean Centre for Climate Change(CMCC) to the specific locations of rainfall stations in Ethiopia for the period 1980–2020. Across the stations, the results of NARX exhibit strong associations and reduced errors. The statistical results indicate that, except for the southwestern Ethiopian highlands, the downscaled monthly precipitation data exhibits high skill scores compared to the station records, demonstrating the effectiveness of the NARX approach for predicting local seasonal rainfall in Ethiopia's complex terrain. In addition to this spatial ANN of the summer season precipitation, temperature, as well as the combination of these two variables, show promising results.

Prediction of Porous Media Fluid Flow with Spatial Heterogeneity Using Criss-Cross Physics-Informed Convolutional Neural Networks

Recent advances in deep neural networks have shed new light on physics,engineering,and scientific computing.Reconciling the data-centered viewpoint with physical simulation is one of the research hotspots.The physicsinformedneural network(PINN)is currently the most general framework,which is more popular due to theconvenience of constructing NNs and excellent generalization ability.The automatic differentiation(AD)-basedPINN model is suitable for the homogeneous scientific problem;however,it is unclear how AD can enforce fluxcontinuity across boundaries between cells of different properties where spatial heterogeneity is represented bygrid cells with different physical properties.In this work,we propose a criss-cross physics-informed convolutionalneural network(CC-PINN)learning architecture,aiming to learn the solution of parametric PDEs with spatialheterogeneity of physical properties.To achieve the seamless enforcement of flux continuity and integration ofphysicalmeaning into CNN,a predefined 2D convolutional layer is proposed to accurately express transmissibilitybetween adjacent cells.The efficacy of the proposedmethodwas evaluated through predictions of several petroleumreservoir problems with spatial heterogeneity and compared against state-of-the-art(PINN)through numericalanalysis as a benchmark,which demonstrated the superiority of the proposed method over the PINN.

RWNeRF:Robust Watermarking Scheme for Neural Radiance Fields Based on Invertible Neural Networks

As neural radiance fields continue to advance in 3D content representation,the copyright issues surrounding 3D models oriented towards implicit representation become increasingly pressing.In response to this challenge,this paper treats the embedding and extraction of neural radiance field watermarks as inverse problems of image transformations and proposes a scheme for protecting neural radiance field copyrights using invertible neural network watermarking.Leveraging 2D image watermarking technology for 3D scene protection,the scheme embeds watermarks within the training images of neural radiance fields through the forward process in invertible neural networks and extracts them from images rendered by neural radiance fields through the reverse process,thereby ensuring copyright protection for both the neural radiance fields and associated 3D scenes.However,challenges such as information loss during rendering processes and deliberate tampering necessitate the design of an image quality enhancement module to increase the scheme’s robustness.This module restores distorted images through neural network processing before watermark extraction.Additionally,embedding watermarks in each training image enables watermark information extraction from multiple viewpoints.Our proposed watermarking method achieves a PSNR(Peak Signal-to-Noise Ratio)value exceeding 37 dB for images containing watermarks and 22 dB for recovered watermarked images,as evaluated on the Lego,Hotdog,and Chair datasets,respectively.These results demonstrate the efficacy of our scheme in enhancing copyright protection.